How to store cut vegetables?!

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I store mine in a big jar of saltwater in the fridge. Salt stops the growth of the bacteria that rots the veggie.
Just rinse them well to remove excess salt before using. They will keep for days, even a week. It keeps them crispy and fresher than just storing in a covered container or zippie bag. Never store them uncovered or open to the air.
This works best for carrot sticks, celery, radishes, the harder veggies. Things like green pepper and cucumber it's more like 3-4 days. Tomatoes don't keep well this way though, too soft. cover those with saran wrap, it'll last maybe 2 days at most. You can mix the veggies in the saltwater, I do.
Try turning up the temp in the fridge if stuff freezes. Almost all fridges have a temp control knob.